Subgroups — #23777235

Order 10112.

1152 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19099266	C₂	1	1	yes	maximal, characteristic, complemented
2	#19099264	C₂	1	2	yes	maximal, complemented
3	#19099263	C₂	1	1	yes	maximal, characteristic, complemented
4	#19099257	C₂	1	2	yes	maximal, complemented
5	#19099254	C₂	1	1	yes	maximal, characteristic, complemented
6	#19099251	C₂	1	1	yes	maximal, characteristic, complemented
7	#19099238	C₂	1	2	yes	maximal, complemented
8	#19099237	C₂	1	2	yes	maximal, complemented
9	#19099225	C₂	1	1	yes	maximal, characteristic, complemented
10	#19099221	C₂	1	1	yes	maximal, characteristic, complemented
11	#19099208	C₂	1	1	yes	maximal, characteristic, complemented
12	#19099206	C₂	1	1	yes	maximal, characteristic, complemented
13	#19099157	C₂	1	2	yes	maximal, complemented
14	#19099146	C₂	1	2	yes	maximal, complemented
15	#19099124	C₂	1	2	yes	maximal, complemented
16	#19099097	C₂	1	1	yes	maximal, characteristic, complemented
17	#19099076	C₂	1	1	yes	maximal, characteristic, complemented
18	#19099073	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²⋊Q₈×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
20	#121×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
21	#19099035	C₂	1	2	yes	maximal, complemented
22	C₂×C₄×D₃₁₆	C₂	1	1	yes	maximal, characteristic, complemented
23	#529×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11929625	C₂²	1	1	yes	characteristic, complemented
25	C₂×#11929623	C₂²	1	1	yes	characteristic, complemented
26	C₂×Q₈×D₇₉	C₂²	1	1	yes	characteristic, complemented
27	C₂²×D₃₁₆	C₂²	1	1	yes	characteristic
28	C₂×D₄×D₇₉	C₂²	1	2	yes	—
29	C₂×D₄×D₇₉	C₂²	1	1	yes	characteristic, complemented
30	C₂²×C₄×D₇₉	C₂²	1	1	yes	characteristic
31	C₂²×C₄×D₇₉	C₂²	1	1	yes	characteristic, complemented
32	#14579156	C₂²	1	2	yes	complemented
33	#14579156	C₂²	1	2	yes	complemented
34	#14579155	C₂²	1	2	yes	complemented
35	#14579155	C₂²	1	2	yes	complemented
36	#14579154	C₂²	1	2	yes	complemented
37	#14579153	C₂²	1	1	yes	characteristic, complemented
38	#14579152	C₂²	1	2	yes	complemented
39	#14579151	C₂²	1	2	yes	complemented
40	#14579149	C₂²	1	2	yes	complemented
41	#14579149	C₂²	1	1	yes	characteristic, complemented
42	#14579147	C₂²	1	2	yes	complemented
43	#14579146	C₂²	1	2	yes	—
44	#14579146	C₂²	1	2	yes	—
45	#14579146	C₂²	1	2	yes	complemented
46	#14579146	C₂²	1	2	yes	complemented
47	#14579145	C₂²	1	2	yes	complemented
48	#14579144	C₂²	1	2	yes	complemented
49	#14579144	C₂²	1	2	yes	complemented
50	#14579143	C₂²	1	2	yes	complemented
51	#14579143	C₂²	1	2	yes	complemented
52	#14579141	C₂²	1	2	yes	complemented
53	#14579141	C₂²	1	1	yes	characteristic, complemented
54	#14579141	C₂²	1	1	yes	characteristic, complemented
55	#14579140	C₂²	1	1	yes	characteristic, complemented
56	#14579139	C₂²	1	2	yes	complemented
57	#14579138	C₂²	1	2	yes	complemented
58	#14579138	C₂²	1	2	yes	complemented
59	#14579137	C₂²	1	1	yes	characteristic, complemented
60	#14579137	C₂²	1	1	yes	characteristic, complemented
61	#14579136	C₂²	1	1	yes	characteristic, complemented
62	#14579136	C₂²	1	2	yes	complemented
63	#14579136	C₂²	1	1	yes	characteristic, complemented
64	#14579136	C₂²	1	2	yes	complemented
65	#14579135	C₂²	1	1	yes	characteristic
66	#14579135	C₂²	1	2	yes	complemented
67	#14579134	C₂²	1	2	yes	complemented
68	#14579134	C₂²	1	2	yes	complemented
69	#14579134	C₂²	1	2	yes	complemented
70	#14579134	C₂²	1	2	yes	complemented
71	#14579133	C₂²	1	2	yes	—
72	#14579132	C₂²	1	1	yes	characteristic, complemented
73	#14579132	C₂²	1	1	yes	characteristic, complemented
74	#14579131	C₂²	1	2	yes	—
75	#14579131	C₂²	1	2	yes	—
76	#14579131	C₂²	1	2	yes	complemented
77	#14579129	C₂²	1	2	yes	complemented
78	C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic, complemented
79	C₄×D₃₁₆	C₂²	1	1	yes	characteristic
80	C₄×D₃₁₆	C₂²	1	1	yes	characteristic
81	C₄×D₃₁₆	C₂²	1	1	yes	characteristic
82	C₄×D₃₁₆	C₂²	1	1	yes	characteristic
83	C₄×D₃₁₆	C₂²	1	1	yes	characteristic, complemented
84	C₄×D₃₁₆	C₂²	1	1	yes	characteristic, complemented
85	C₄×D₃₁₆	C₂²	1	2	yes	complemented
86	C₄×D₃₁₆	C₂²	1	1	yes	characteristic, complemented
87	C₄×D₃₁₆	C₂²	1	1	yes	characteristic, complemented
88	C₄×D₃₁₆	C₂²	1	1	yes	characteristic, complemented
89	D₄×Dic₇₉	C₂²	1	2	yes	complemented
90	#14579123	C₂²	1	2	yes	complemented
91	#14579123	C₂²	1	2	yes	complemented
92	C₄×C₂²⋊D₇₉	C₂²	1	2	yes	complemented
93	C₄×C₂²⋊D₇₉	C₂²	1	2	yes	complemented
94	(C₂²⋊D₇₉)⋊C₄	C₂²	1	2	yes	complemented
95	(C₂²⋊D₇₉)⋊C₄	C₂²	1	2	yes	complemented
96	(C₂²⋊D₇₉)⋊C₄	C₂²	1	2	yes	complemented
97	#14579119	C₂²	1	2	yes	complemented
98	#14579119	C₂²	1	1	yes	characteristic, complemented
99	#14579119	C₂²	1	1	yes	characteristic, complemented
100	#14579118	C₂²	1	2	yes	complemented
101	#14579118	C₂²	1	2	yes	complemented
102	C₂×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic, complemented
103	C₄⋊C₄×D₇₉	C₂²	1	1	yes	characteristic, complemented
104	C₄⋊C₄×D₇₉	C₂²	1	2	yes	complemented
105	C₄⋊C₄×D₇₉	C₂²	1	1	yes	characteristic, complemented
106	C₂×(C₂×D₇₉)⋊C₄	C₂²	1	1	yes	characteristic
107	C₂×(C₂×D₇₉)⋊C₄	C₂²	1	1	yes	characteristic, complemented
108	C₂×(C₂×D₇₉)⋊C₄	C₂²	1	2	yes	complemented
109	C₂²⋊C₄×D₇₉	C₂²	1	2	yes	—
110	C₂²⋊C₄×D₇₉	C₂²	1	2	yes	complemented
111	C₂²⋊C₄×D₇₉	C₂²	1	2	yes	complemented
112	#126×C₇₉	C₂²	1	2	yes	complemented
113	#125×C₇₉	C₂²	1	1	yes	characteristic, complemented
114	#124×C₇₉	C₂²	1	1	yes	characteristic, complemented
115	#123×C₇₉	C₂²	1	2	yes	complemented
116	C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
117	#121×C₇₉	C₂²	1	1	yes	characteristic
118	C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₇₉	C₂²	1	2	yes	complemented
120	C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
121	#117×C₇₉	C₂²	1	2	yes	complemented
122	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₇₉	C₂³	1	2	yes	—
124	C₂³×D₇₉	C₂³	1	1	yes	characteristic
125	C₂³×D₇₉	C₂³	1	1	yes	characteristic
126	#11929625	—	4	2	no	—
127	#11929623	—	4	2	no	—
128	C₂×Dic₁₅₈	C₂³	1	1	yes	characteristic
129	C₂×Dic₁₅₈	C₂³	1	2	yes	—
130	Q₈×D₇₉	—	4	2	no	—
131	C₂×D₃₁₆	—	2	4	no	—
132	C₂×D₃₁₆	C₂³	1	1	yes	characteristic
133	C₂×D₃₁₆	C₂³	1	2	yes	—
134	C₂×D₃₁₆	C₂³	1	1	yes	characteristic
135	C₂×D₃₁₆	C₂³	1	1	yes	characteristic
136	C₂×D₃₁₆	C₂³	1	1	yes	characteristic
137	C₂×D₃₁₆	C₂³	1	1	yes	characteristic
138	C₂×D₃₁₆	C₂³	1	2	yes	—
139	C₂×D₃₁₆	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₇₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₇₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₇₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₇₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₇₉	C₂³	1	2	yes	—
145	D₄×D₇₉	—	2	8	no	—
146	D₄×D₇₉	—	4	2	no	—
147	C₂²×Dic₇₉	C₂³	1	2	yes	—
148	C₂²×Dic₇₉	C₂³	1	1	yes	characteristic
149	C₂²×Dic₇₉	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₇₉	—	4	2	no	—
151	C₂×C₄×D₇₉	—	4	2	no	—
152	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₇₉	C₂³	1	2	yes	—
156	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₇₉	C₂³	1	2	yes	—
158	C₂×C₄×D₇₉	C₂³	1	2	yes	—
159	C₂×C₄×D₇₉	C₂³	1	2	yes	—
160	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₇₉	C₂³	1	2	yes	—
162	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
163	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
164	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
165	C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
166	C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
167	C₄⋊Dic₇₉	C₂³	1	2	yes	—
168	C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
169	C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
170	C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
171	C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
172	C₄⋊Dic₇₉	C₂³	1	2	yes	—
173	Dic₇₉⋊C₄	C₂³	1	2	yes	—
174	Dic₇₉⋊C₄	C₂³	1	2	yes	—
175	Dic₇₉⋊C₄	C₂³	1	2	yes	—
176	Dic₇₉⋊C₄	C₂³	1	2	yes	—
177	Dic₇₉⋊C₄	C₂³	1	2	yes	—
178	Dic₇₉⋊C₄	C₂³	1	2	yes	—
179	Dic₇₉⋊C₄	C₂³	1	2	yes	—
180	Dic₇₉⋊C₄	C₂³	1	2	yes	—
181	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
182	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
183	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
184	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₇₉)⋊C₄	C₂³	1	1	yes	characteristic
187	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₇₉)⋊C₄	C₂³	1	1	yes	characteristic
190	(C₂×D₇₉)⋊C₄	C₂³	1	1	yes	characteristic
191	(C₂×D₇₉)⋊C₄	C₂³	1	1	yes	characteristic
192	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₇₉)⋊C₄	C₂³	1	1	yes	characteristic
195	(C₂×D₇₉)⋊C₄	C₂³	1	1	yes	characteristic
196	(C₂×D₇₉)⋊C₄	C₂³	1	1	yes	characteristic
197	(C₂×D₇₉)⋊C₄	C₂³	1	1	yes	characteristic
198	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
199	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
200	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
201	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
202	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
203	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
204	C₄×Dic₇₉	C₂³	1	2	yes	—
205	C₄×Dic₇₉	C₂³	1	2	yes	—
206	C₄×Dic₇₉	C₂³	1	2	yes	—
207	C₂×Q₈×C₇₉	C₂³	1	1	yes	characteristic
208	C₂×D₄×C₇₉	C₂³	1	1	yes	characteristic
209	C₂×D₄×C₇₉	C₂³	1	2	yes	—
210	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
211	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
212	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
213	C₂²×C₄×C₇₉	C₂³	1	2	yes	—
214	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
215	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
216	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
218	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
219	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
225	C₄²×C₇₉	C₂³	1	1	yes	characteristic
226	C₄²×C₇₉	C₂³	1	1	yes	characteristic
227	C₄²×C₇₉	C₂³	1	1	yes	characteristic
228	C₄²×C₇₉	C₂³	1	1	yes	characteristic
229	C₄²×C₇₉	C₂³	1	2	yes	—
230	C₂³×C₇₉	C₂⁴	1	2	yes	—
231	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
232	C₂²×D₇₉	—	2	2	no	—
233	C₂²×D₇₉	—	2	4	no	—
234	C₂²×D₇₉	—	4	1	no	—
235	C₂²×D₇₉	—	4	1	no	—
236	C₂²×D₇₉	—	4	1	no	—
237	C₂²×D₇₉	—	4	1	no	—
238	C₂²×D₇₉	—	4	2	no	—
239	C₂²×D₇₉	—	4	2	no	—
240	C₂²×D₇₉	#41	1	4	yes	complemented
241	C₂²×D₇₉	C₂⁴	1	2	yes	—
242	C₂²×D₇₉	C₂⁴	1	1	yes	characteristic
243	C₂²×D₇₉	C₂⁴	1	1	yes	characteristic
244	C₂²×D₇₉	C₂⁴	1	1	yes	characteristic
245	C₂²×D₇₉	C₂⁴	1	1	yes	characteristic
246	Q₈×C₇₉	—	2	2	no	—
247	D₄×C₇₉	—	2	4	no	—
248	D₄×C₇₉	—	2	2	no	—
249	C₂×C₄×C₇₉	—	2	2	no	—
250	C₂×C₄×C₇₉	—	2	2	no	—
251	C₂×C₄×C₇₉	—	4	1	no	—
252	C₂×C₄×C₇₉	—	4	2	no	—
253	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
255	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
256	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
259	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
260	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
261	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
262	C₂²⋊D₇₉	—	2	4	no	—
263	C₂²⋊D₇₉	—	2	4	no	—
264	C₂²⋊D₇₉	—	4	2	no	—
265	C₂²⋊D₇₉	—	4	2	no	—
266	C₂²⋊D₇₉	—	4	2	no	—
267	C₂×Dic₇₉	—	4	1	no	—
268	C₂×Dic₇₉	—	4	1	no	—
269	C₂×Dic₇₉	—	4	2	no	—
270	C₂×Dic₇₉	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₇₉	C₂⁴	1	2	yes	—
272	C₂×Dic₇₉	C₂⁴	1	1	yes	characteristic
273	C₂×Dic₇₉	C₂⁴	1	2	yes	—
274	C₂×Dic₇₉	C₂⁴	1	2	yes	—
275	C₂×Dic₇₉	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₇₉	C₂⁴	1	1	yes	characteristic
277	D₃₁₆	—	2	4	no	—
278	D₃₁₆	—	2	2	no	—
279	D₃₁₆	—	2	2	no	—
280	D₃₁₆	—	2	2	no	—
281	D₃₁₆	—	2	2	no	—
282	D₃₁₆	—	2	2	no	—
283	D₃₁₆	—	4	2	no	—
284	D₃₁₆	—	4	2	no	—
285	C₄×D₇₉	—	2	4	no	—
286	C₄×D₇₉	—	2	2	no	—
287	C₄×D₇₉	—	2	2	no	—
288	C₄×D₇₉	—	2	2	no	—
289	C₄×D₇₉	—	2	2	no	—
290	C₄×D₇₉	—	4	1	no	—
291	C₄×D₇₉	—	4	1	no	—
292	C₄×D₇₉	—	4	1	no	—
293	C₄×D₇₉	—	4	1	no	—
294	C₄×D₇₉	—	4	2	no	—
295	C₄×D₇₉	—	4	2	no	—
296	C₄×D₇₉	—	4	2	no	—
297	C₄×D₇₉	—	4	2	no	—
298	Dic₁₅₈	—	2	2	no	—
299	Dic₁₅₈	—	4	2	no	—
300	C₂²×C₇₉	—	2	1	no	—
301	C₂²×C₇₉	—	2	1	no	—
302	C₂²×C₇₉	—	2	2	no	—
303	C₂²×C₇₉	—	2	2	no	—
304	C₂²×C₇₉	—	2	2	no	—
305	C₂²×C₇₉	C₂×#41	1	2	yes	—
306	C₂²×C₇₉	C₂⁵	1	1	yes	characteristic
307	C₂×D₇₉	—	2	1	no	—
308	C₂×D₇₉	—	2	1	no	—
309	C₂×D₇₉	—	2	1	no	—
310	C₂×D₇₉	—	2	1	no	—
311	C₂×D₇₉	—	2	2	no	—
312	C₂×D₇₉	—	2	1	no	—
313	C₂×D₇₉	—	2	1	no	—
314	C₂×D₇₉	—	2	1	no	—
315	C₂×D₇₉	—	2	2	no	—
316	C₂×D₇₉	—	2	1	no	—
317	C₂×D₇₉	—	2	1	no	—
318	C₂×D₇₉	—	2	2	no	—
319	C₂×D₇₉	—	2	1	no	—
320	C₂×D₇₉	—	4	4	no	—
321	C₂×D₇₉	—	4	4	no	—
322	C₂×D₇₉	—	8	4	no	—
323	C₂×D₇₉	C₂×#41	1	2	yes	—
324	C₂×D₇₉	C₂×#41	1	2	yes	—
325	C₄×C₇₉	—	2	1	no	—
326	C₄×C₇₉	—	2	1	no	—
327	C₄×C₇₉	—	2	2	no	—
328	C₄×C₇₉	—	2	1	no	—
329	C₄×C₇₉	—	2	2	no	—
330	C₄×C₇₉	—	2	1	no	—
331	C₄×C₇₉	—	2	1	no	—
332	C₄×C₇₉	—	2	2	no	—
333	C₄×C₇₉	H(5,𝔽₂)	1	2	yes	—
334	Dic₇₉	—	2	2	no	—
335	Dic₇₉	—	2	1	no	—
336	Dic₇₉	—	2	2	no	—
337	Dic₇₉	—	2	1	no	—
338	Dic₇₉	—	2	1	no	—
339	Dic₇₉	—	2	1	no	—
340	Dic₇₉	—	2	2	no	—
341	C₂×C₇₉	—	2	2	no	—
342	C₂×C₇₉	—	4	2	no	—
343	C₂×C₇₉	C₂²×#41	1	1	yes	characteristic
344	C₂×C₇₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
345	C₂×C₇₉	#585	1	1	yes	characteristic
346	D₇₉	—	2	2	no	—
347	D₇₉	—	2	2	no	—
348	D₇₉	—	4	1	no	—
349	D₇₉	—	4	1	no	—
350	D₇₉	—	4	2	no	—
351	#3505	—	79	1	no	maximal, Sylow
352	C₇₉	#3505	1	1	yes	characteristic, complemented, Sylow
353	#553	—	79	2	no	—
354	#553	—	79	1	no	—
355	#553	—	79	1	no	—
356	#553	—	79	2	no	—
357	#552	—	79	1	no	—
358	#552	—	79	1	no	—
359	#551	—	79	2	no	—
360	#551	—	79	2	no	—
361	#548	—	79	1	no	—
362	#548	—	79	1	no	—
363	#546	—	79	1	no	—
364	#546	—	79	1	no	—
365	#539	—	79	2	no	—
366	#538	—	79	2	no	—
367	#534	—	79	2	no	—
368	#529	—	79	1	no	—
369	#529	D₇₉	1	1	yes	characteristic, complemented
370	#525	—	79	1	no	—
371	#525	—	79	1	no	—
372	C₂×C₂²⋊Q₈	—	79	1	no	—
373	C₂×#121	—	79	1	no	—
374	#518	—	79	2	no	—
375	C₂×C₄×D₄	—	79	1	no	—
376	C₂×#41	—	79	1	no	—
377	C₂×#41	—	79	1	no	—
378	C₂²×Q₈	—	79	1	no	—
379	C₂²×D₄	—	79	1	no	—
380	C₂²×D₄	—	79	2	no	—
381	C₂²×D₄	—	79	1	no	—
382	C₂³×C₄	—	79	1	no	—
383	C₂³×C₄	—	79	1	no	—
384	#126	—	79	2	no	—
385	#126	—	79	2	no	—
386	#126	—	79	2	no	—
387	#126	—	79	2	no	—
388	#126	—	79	2	no	—
389	#126	C₂×D₇₉	1	2	yes	complemented
390	#125	—	79	2	no	—
391	#125	—	79	2	no	—
392	#125	—	79	1	no	—
393	#125	C₂×D₇₉	1	1	yes	characteristic, complemented
394	#124	—	79	2	no	—
395	#124	—	79	1	no	—
396	#124	—	79	2	no	—
397	#124	C₂×D₇₉	1	1	yes	characteristic, complemented
398	#123	—	79	2	no	—
399	#123	—	79	2	no	—
400	#123	—	79	2	no	—
401	#123	—	79	2	no	—
402	#123	—	79	2	no	—
403	#123	—	79	2	no	—
404	#123	—	79	2	no	—
405	#123	—	79	2	no	—
406	#123	—	79	2	no	—
407	#123	C₂×D₇₉	1	2	yes	complemented
408	C₂²⋊Q₈	—	79	1	no	—
409	C₂²⋊Q₈	—	79	1	no	—
410	C₂²⋊Q₈	—	79	1	no	—
411	C₂²⋊Q₈	—	79	1	no	—
412	C₂²⋊Q₈	—	79	2	no	—
413	C₂²⋊Q₈	—	79	1	no	—
414	C₂²⋊Q₈	—	79	2	no	—
415	C₂²⋊Q₈	—	79	2	no	—
416	C₂²⋊Q₈	—	79	2	no	—
417	C₂²⋊Q₈	C₂×D₇₉	1	1	yes	characteristic, complemented
418	#121	—	79	2	no	—
419	#121	—	79	1	no	—
420	#121	—	79	1	no	—
421	#121	—	79	1	no	—
422	#121	—	79	2	no	—
423	#121	—	79	1	no	—
424	#121	—	79	1	no	—
425	#121	—	79	2	no	—
426	#121	—	79	2	no	—
427	#121	—	79	2	no	—
428	#121	—	79	2	no	—
429	#121	—	79	2	no	—
430	#121	—	79	2	no	—
431	#121	C₂×D₇₉	1	1	yes	characteristic
432	#120	—	79	2	no	—
433	#120	—	79	2	no	—
434	#120	—	79	2	no	—
435	#120	—	79	2	no	—
436	C₄×Q₈	—	79	1	no	—
437	C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic, complemented
438	C₄×D₄	—	79	2	no	—
439	C₄×D₄	—	79	2	no	—
440	C₄×D₄	—	79	2	no	—
441	C₄×D₄	—	79	2	no	—
442	C₄×D₄	—	79	2	no	—
443	C₄×D₄	—	79	2	no	—
444	C₄×D₄	—	79	2	no	—
445	C₄×D₄	—	79	2	no	—
446	C₄×D₄	—	79	1	no	—
447	C₄×D₄	—	79	1	no	—
448	C₄×D₄	—	79	1	no	—
449	C₄×D₄	—	79	1	no	—
450	C₄×D₄	—	79	1	no	—
451	C₄×D₄	—	79	1	no	—
452	C₄×D₄	—	79	1	no	—
453	C₄×D₄	—	79	1	no	—
454	C₄×D₄	—	79	2	no	—
455	C₄×D₄	—	79	1	no	—
456	C₄×D₄	C₂×D₇₉	1	2	yes	complemented
457	C₄×D₄	C₂×D₇₉	1	1	yes	characteristic, complemented
458	#117	—	79	2	no	—
459	#117	—	79	1	no	—
460	#117	—	79	1	no	—
461	#117	—	79	2	no	—
462	#117	—	79	2	no	—
463	#117	C₂×D₇₉	1	2	yes	complemented
464	C₂×C₄⋊C₄	—	79	1	no	—
465	C₂×C₄⋊C₄	—	79	1	no	—
466	C₂×C₄⋊C₄	—	79	2	no	—
467	C₂×C₄⋊C₄	—	79	1	no	—
468	C₂×C₂²⋊C₄	—	79	1	no	—
469	C₂×C₂²⋊C₄	—	79	1	no	—
470	C₂×C₂²⋊C₄	—	79	2	no	—
471	C₂×C₂²⋊C₄	—	79	2	no	—
472	C₂×C₂²⋊C₄	—	79	2	no	—
473	C₂×C₂²⋊C₄	—	79	2	no	—
474	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic, complemented
475	C₂⁴	—	79	1	no	—
476	C₂⁴	—	79	2	no	—
477	C₂⁴	—	79	1	no	—
478	#41	—	316	2	no	—
479	#41	—	316	2	no	—
480	C₂×Q₈	—	316	2	no	—
481	C₂×Q₈	—	79	2	no	—
482	C₂×Q₈	—	79	1	no	—
483	C₂×Q₈	C₂²×D₇₉	1	1	yes	characteristic
484	C₂×D₄	—	316	2	no	—
485	C₂×D₄	—	79	2	no	—
486	C₂×D₄	—	79	2	no	—
487	C₂×D₄	—	79	2	no	—
488	C₂×D₄	—	79	2	no	—
489	C₂×D₄	—	79	2	no	—
490	C₂×D₄	—	79	2	no	—
491	C₂×D₄	—	79	2	no	—
492	C₂×D₄	—	79	1	no	—
493	C₂×D₄	—	79	1	no	—
494	C₂×D₄	—	79	2	no	—
495	C₂×D₄	—	79	1	no	—
496	C₂×D₄	—	79	1	no	—
497	C₂×D₄	—	79	1	no	—
498	C₂×D₄	—	158	4	no	—
499	C₂×D₄	—	158	8	no	—
500	C₂×D₄	C₂²×D₇₉	1	2	yes	—
501	C₂×D₄	C₂²×D₇₉	1	1	yes	characteristic
502	C₂²×C₄	—	316	2	no	—
503	C₂²×C₄	—	316	2	no	—
504	C₂²×C₄	—	79	1	no	—
505	C₂²×C₄	—	79	1	no	—
506	C₂²×C₄	—	79	2	no	—
507	C₂²×C₄	—	79	1	no	—
508	C₂²×C₄	—	79	2	no	—
509	C₂²×C₄	—	79	2	no	—
510	C₂²×C₄	—	79	2	no	—
511	C₂²×C₄	—	79	2	no	—
512	C₂²×C₄	—	79	1	no	—
513	C₂²×C₄	—	79	1	no	—
514	C₂²×C₄	—	79	1	no	—
515	C₂²×C₄	—	79	2	no	—
516	C₂²×C₄	—	79	1	no	—
517	C₂²×C₄	—	79	1	no	—
518	C₂²×C₄	—	79	1	no	—
519	C₂²×C₄	—	79	1	no	—
520	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
521	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
522	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
523	C₂²×C₄	C₂²×D₇₉	1	2	yes	—
524	C₄⋊C₄	—	79	2	no	—
525	C₄⋊C₄	—	79	2	no	—
526	C₄⋊C₄	—	79	2	no	—
527	C₄⋊C₄	—	79	2	no	—
528	C₄⋊C₄	—	79	2	no	—
529	C₄⋊C₄	—	79	2	no	—
530	C₄⋊C₄	—	79	2	no	—
531	C₄⋊C₄	—	79	2	no	—
532	C₄⋊C₄	—	79	1	no	—
533	C₄⋊C₄	—	79	1	no	—
534	C₄⋊C₄	—	79	1	no	—
535	C₄⋊C₄	—	79	1	no	—
536	C₄⋊C₄	—	79	1	no	—
537	C₄⋊C₄	—	79	1	no	—
538	C₄⋊C₄	—	79	2	no	—
539	C₄⋊C₄	—	79	2	no	—
540	C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
541	C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
542	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
543	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
544	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
545	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
546	C₂²⋊C₄	—	79	2	no	—
547	C₂²⋊C₄	—	79	2	no	—
548	C₂²⋊C₄	—	79	2	no	—
549	C₂²⋊C₄	—	79	1	no	—
550	C₂²⋊C₄	—	79	1	no	—
551	C₂²⋊C₄	—	79	2	no	—
552	C₂²⋊C₄	—	79	2	no	—
553	C₂²⋊C₄	—	79	2	no	—
554	C₂²⋊C₄	—	79	1	no	—
555	C₂²⋊C₄	—	79	1	no	—
556	C₂²⋊C₄	—	79	1	no	—
557	C₂²⋊C₄	—	79	1	no	—
558	C₂²⋊C₄	—	79	2	no	—
559	C₂²⋊C₄	—	79	2	no	—
560	C₂²⋊C₄	—	79	1	no	—
561	C₂²⋊C₄	—	79	1	no	—
562	C₂²⋊C₄	—	79	2	no	—
563	C₂²⋊C₄	—	79	2	no	—
564	C₂²⋊C₄	—	79	2	no	—
565	C₂²⋊C₄	—	79	2	no	—
566	C₂²⋊C₄	—	79	2	no	—
567	C₂²⋊C₄	—	79	2	no	—
568	C₂²⋊C₄	—	79	2	no	—
569	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
570	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
571	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
572	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
573	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
574	C₄²	—	79	2	no	—
575	C₄²	—	79	2	no	—
576	C₄²	—	79	2	no	—
577	C₄²	C₂²×D₇₉	1	1	yes	characteristic
578	C₄²	C₂²×D₇₉	1	1	yes	characteristic
579	C₄²	C₂²×D₇₉	1	1	yes	characteristic
580	C₄²	C₂²×D₇₉	1	1	yes	characteristic
581	C₄²	C₂²×D₇₉	1	2	yes	—
582	C₂³	—	316	1	no	—
583	C₂³	—	316	1	no	—
584	C₂³	—	316	1	no	—
585	C₂³	—	316	1	no	—
586	C₂³	—	316	2	no	—
587	C₂³	—	316	2	no	—
588	C₂³	—	79	4	no	—
589	C₂³	—	79	1	no	—
590	C₂³	—	79	1	no	—
591	C₂³	—	79	1	no	—
592	C₂³	—	79	1	no	—
593	C₂³	—	79	2	no	—
594	C₂³	—	158	4	no	—
595	C₂³	—	158	2	no	—
596	C₂³	C₂³×D₇₉	1	2	yes	—
597	C₂³	C₂³×D₇₉	1	1	yes	characteristic
598	Q₈	—	2	2	no	—
599	Q₈	—	316	2	no	—
600	Q₈	—	158	2	no	—
601	D₄	—	2	4	no	—
602	D₄	—	2	2	no	—
603	D₄	—	316	2	no	—
604	D₄	—	316	2	no	—
605	D₄	—	316	2	no	—
606	D₄	—	316	2	no	—
607	D₄	—	316	2	no	—
608	D₄	—	158	2	no	—
609	D₄	—	158	2	no	—
610	D₄	—	158	2	no	—
611	D₄	—	158	2	no	—
612	D₄	—	158	4	no	—
613	D₄	—	158	4	no	—
614	D₄	—	158	4	no	—
615	D₄	—	158	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	2	no	—
620	C₂×C₄	—	316	1	no	—
621	C₂×C₄	—	316	1	no	—
622	C₂×C₄	—	316	1	no	—
623	C₂×C₄	—	316	1	no	—
624	C₂×C₄	—	316	2	no	—
625	C₂×C₄	—	316	2	no	—
626	C₂×C₄	—	316	2	no	—
627	C₂×C₄	—	316	2	no	—
628	C₂×C₄	—	316	1	no	—
629	C₂×C₄	—	316	1	no	—
630	C₂×C₄	—	316	2	no	—
631	C₂×C₄	—	79	2	no	—
632	C₂×C₄	—	79	1	no	—
633	C₂×C₄	—	79	1	no	—
634	C₂×C₄	—	79	2	no	—
635	C₂×C₄	—	79	2	no	—
636	C₂×C₄	—	79	1	no	—
637	C₂×C₄	—	79	1	no	—
638	C₂×C₄	—	158	4	no	—
639	C₂×C₄	—	158	2	no	—
640	C₂×C₄	—	158	2	no	—
641	C₂×C₄	—	158	2	no	—
642	C₂×C₄	—	158	2	no	—
643	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
644	C₂×C₄	C₂³×D₇₉	1	2	yes	—
645	C₂×C₄	C₂³×D₇₉	1	2	yes	—
646	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
647	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
648	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
649	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
650	C₂×C₄	C₂³×D₇₉	1	2	yes	—
651	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
652	C₂²	—	2	1	no	—
653	C₂²	—	2	1	no	—
654	C₂²	—	2	2	no	—
655	C₂²	—	2	2	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	316	4	no	—
658	C₂²	—	316	4	no	—
659	C₂²	—	79	2	no	—
660	C₂²	—	79	2	no	—
661	C₂²	—	632	4	no	—
662	C₂²	—	158	1	no	—
663	C₂²	—	158	1	no	—
664	C₂²	—	158	2	no	—
665	C₂²	—	158	2	no	—
666	C₂²	—	158	1	no	—
667	C₂²	—	158	1	no	—
668	C₂²	—	158	1	no	—
669	C₂²	—	158	1	no	—
670	C₂²	—	158	2	no	—
671	C₂²	—	158	1	no	—
672	C₂²	—	158	1	no	—
673	C₂²	—	158	1	no	—
674	C₂²	—	158	1	no	—
675	C₂²	#41×D₇₉	1	2	yes	—
676	C₂²	C₂⁴×D₇₉	1	1	yes	characteristic
677	C₄	—	2	1	no	—
678	C₄	—	2	2	no	—
679	C₄	—	2	1	no	—
680	C₄	—	2	1	no	—
681	C₄	—	2	2	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	2	no	—
685	C₄	—	158	1	no	—
686	C₄	—	158	1	no	—
687	C₄	—	158	1	no	—
688	C₄	—	158	1	no	—
689	C₄	—	158	2	no	—
690	C₄	—	158	2	no	—
691	C₄	—	158	2	no	—
692	C₄	#14579207	1	2	yes	—
693	C₂	—	2	2	no	—
694	C₂	—	4	2	no	—
695	C₂	—	316	1	no	—
696	C₂	—	316	1	no	—
697	C₂	—	316	2	no	—
698	C₂	—	158	2	no	—
699	C₂	—	158	2	no	—
700	C₂	C₂×#41×D₇₉	1	1	yes	characteristic
701	C₂	C₂×#14579207	1	1	yes	characteristic
702	C₂	#19099399	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇₉
commutator, socle, cosocle	C₂²×C₇₉	C₂⁵
Fitting	#529×C₇₉	C₂
hypercenter	#529	D₇₉
hypocenter	C₇₉	#3505
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ #529

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #19099266	C₂	semidirect
2. #19099264	C₂	semidirect
3. #19099263	C₂	semidirect
4. #19099257	C₂	semidirect
5. #19099254	C₂	semidirect
6. #19099251	C₂	semidirect
7. #19099238	C₂	semidirect
8. #19099237	C₂	semidirect
9. #19099225	C₂	semidirect
10. #19099221	C₂	semidirect
11. #19099208	C₂	semidirect
12. #19099206	C₂	semidirect
13. #19099157	C₂	semidirect
14. #19099146	C₂	semidirect
15. #19099124	C₂	semidirect
16. #19099097	C₂	semidirect
17. #19099076	C₂	semidirect
18. #19099073	C₂	semidirect
19. C₂²⋊Q₈×D₇₉	C₂	semidirect
20. #121×D₇₉	C₂	semidirect
21. #19099035	C₂	semidirect
22. C₂×C₄×D₃₁₆	C₂	semidirect
23. #529×C₇₉	C₂	semidirect
24. C₂×#11929625	C₂²	semidirect
25. C₂×#11929623	C₂²	semidirect
26. C₂×Q₈×D₇₉	C₂²	semidirect
29. C₂×D₄×D₇₉	C₂²	semidirect
31. C₂²×C₄×D₇₉	C₂²	semidirect
32. #14579156	C₂²	semidirect
33. #14579156	C₂²	semidirect
34. #14579155	C₂²	semidirect
35. #14579155	C₂²	semidirect
36. #14579154	C₂²	semidirect
37. #14579153	C₂²	semidirect
38. #14579152	C₂²	semidirect
39. #14579151	C₂²	semidirect
40. #14579149	C₂²	semidirect
41. #14579149	C₂²	semidirect
42. #14579147	C₂²	semidirect
45. #14579146	C₂²	semidirect
46. #14579146	C₂²	semidirect
47. #14579145	C₂²	semidirect
48. #14579144	C₂²	semidirect
49. #14579144	C₂²	semidirect
50. #14579143	C₂²	semidirect
51. #14579143	C₂²	semidirect
52. #14579141	C₂²	semidirect
53. #14579141	C₂²	semidirect
54. #14579141	C₂²	semidirect
55. #14579140	C₂²	semidirect
56. #14579139	C₂²	semidirect
57. #14579138	C₂²	semidirect
58. #14579138	C₂²	semidirect
59. #14579137	C₂²	semidirect
60. #14579137	C₂²	semidirect
61. #14579136	C₂²	semidirect
62. #14579136	C₂²	semidirect
63. #14579136	C₂²	semidirect
64. #14579136	C₂²	semidirect
66. #14579135	C₂²	semidirect
67. #14579134	C₂²	semidirect
68. #14579134	C₂²	semidirect
69. #14579134	C₂²	semidirect
70. #14579134	C₂²	semidirect
72. #14579132	C₂²	semidirect
73. #14579132	C₂²	semidirect
76. #14579131	C₂²	semidirect
77. #14579129	C₂²	semidirect
78. C₄×Dic₁₅₈	C₂²	semidirect
83. C₄×D₃₁₆	C₂²	semidirect
84. C₄×D₃₁₆	C₂²	semidirect
85. C₄×D₃₁₆	C₂²	semidirect
86. C₄×D₃₁₆	C₂²	semidirect
87. C₄×D₃₁₆	C₂²	semidirect
88. C₄×D₃₁₆	C₂²	semidirect
89. D₄×Dic₇₉	C₂²	semidirect
90. #14579123	C₂²	semidirect
91. #14579123	C₂²	semidirect
92. C₄×C₂²⋊D₇₉	C₂²	semidirect
93. C₄×C₂²⋊D₇₉	C₂²	semidirect
94. (C₂²⋊D₇₉)⋊C₄	C₂²	semidirect
95. (C₂²⋊D₇₉)⋊C₄	C₂²	semidirect
96. (C₂²⋊D₇₉)⋊C₄	C₂²	semidirect
97. #14579119	C₂²	semidirect
98. #14579119	C₂²	semidirect
99. #14579119	C₂²	semidirect
100. #14579118	C₂²	semidirect
101. #14579118	C₂²	semidirect
102. C₂×C₄⋊Dic₇₉	C₂²	semidirect
103. C₄⋊C₄×D₇₉	C₂²	semidirect
104. C₄⋊C₄×D₇₉	C₂²	semidirect
105. C₄⋊C₄×D₇₉	C₂²	semidirect
107. C₂×(C₂×D₇₉)⋊C₄	C₂²	semidirect
108. C₂×(C₂×D₇₉)⋊C₄	C₂²	semidirect
110. C₂²⋊C₄×D₇₉	C₂²	semidirect
111. C₂²⋊C₄×D₇₉	C₂²	semidirect
112. #126×C₇₉	C₂²	semidirect
113. #125×C₇₉	C₂²	semidirect
114. #124×C₇₉	C₂²	semidirect
115. #123×C₇₉	C₂²	semidirect
116. C₂²⋊Q₈×C₇₉	C₂²	semidirect
118. C₄×Q₈×C₇₉	C₂²	semidirect
119. C₄×D₄×C₇₉	C₂²	semidirect
120. C₄×D₄×C₇₉	C₂²	semidirect
121. #117×C₇₉	C₂²	semidirect
122. C₂×C₄²×C₇₉	C₂²	semidirect
240. C₂²×D₇₉	#41	semidirect
352. C₇₉	#3505	semidirect
369. #529	D₇₉	semidirect
389. #126	C₂×D₇₉	semidirect
393. #125	C₂×D₇₉	semidirect
397. #124	C₂×D₇₉	semidirect
407. #123	C₂×D₇₉	semidirect
417. C₂²⋊Q₈	C₂×D₇₉	semidirect
437. C₄×Q₈	C₂×D₇₉	semidirect
456. C₄×D₄	C₂×D₇₉	semidirect
457. C₄×D₄	C₂×D₇₉	semidirect
463. #117	C₂×D₇₉	semidirect
474. C₂×C₄²	C₂×D₇₉	semidirect